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Retired Moderator V
Joined: 27 Oct 2017
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If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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Question Stats: 62% (01:17) correct 38% (01:06) wrong based on 99 sessions

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If $$y ≠ 0$$, is x = -1 ?

(1) $$x = \frac{y}{|y|}$$

(2) $$|x| = -x$$

GMATBuster's Collection

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Originally posted by gmatbusters on 29 Jun 2019, 20:23.
Last edited by Bunuel on 30 Jun 2019, 03:57, edited 1 time in total.
Renamed the topic.
Intern  B
Joined: 26 Jun 2019
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Location: India
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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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1
1
So, the question starts with two variables, x and y both of which don't have any numerical value attached to them. Only y cannot be 0.

Solving for 1.
X = y/mod(y)
Now if y is positive answer is 1
If y is negative answer would be - 1

Hence not sufficient.

Solving for 2.
Here mod(x) = - (x) is only possible when x is any negative number.
It's proven that x is negatice but not - 1, it could be any negative number.

Hence not sufficient.

Now solving for both together, we get that x can only be 1 or - 1 from the first statement and that x can only be negative from second.

Which means x can only be - 1.
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Senior Manager  G
Joined: 25 Feb 2019
Posts: 333
Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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IMO A

x = y/|y|

when y <0 , we get x = 1

when y y>0 , we get x = 1

so clear anser No

sufficient

statement 2 says x <0 , but can be be anything

so not sufficient

IMO A

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Intern  B
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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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m1033512 wrote:
IMO A

x = y/|y|

when y <0 , we get x = 1

when y y>0 , we get x = 1

so clear anser No

sufficient

statement 2 says x <0 , but can be be anything

so not sufficient

IMO A

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m1033512 I believe when y<0, x = $$\frac{y}{|y|}$$ would give us -1
Senior Manager  G
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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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we will have both as -y in numerator and denomintor both

it will cancel out to 1

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Intern  B
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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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m1033512 wrote:
we will have both as -y in numerator and denomintor both

it will cancel out to 1

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m1033512
Friend we'll only have -y in the denominator, not the numerator. Numberator will stay y(which has been defined as negative by us)

for eg:- let y be -5
$$\frac{y}{|y|} = \frac{-5}{|-5|}$$
=-5/5
=-1
Senior Manager  G
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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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but I defined two cases for y ( removed the mod)

first

y<0 , then both are negative, and will take the same value so 1

second y > 0 , both are positive and will take the same value so 1

so for any y != 0, we always get 1

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Intern  B
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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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m1033512 wrote:
but I defined two cases for y ( removed the mod)

first

y<0 , then both are negative, and will take the same value so 1

second y > 0 , both are positive and will take the same value so 1

so for any y != 0, we always get 1

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m1033512

Friend, I agree that you've defined two cases for y
for y > 0 it is clearly 1

but I'm talking about the case where you have taken y < 0

$$\frac{y}{|y|}$$ for any number less than 0 will give us -1

I believe the mistake you're making is while removing mod; I believe you are multiplying both the numerator as well as the denominator with a -ve in the process, which you shouldn't as there is only 1 mod that is being removed.

Try solving X*|Y| = Y for any negative Y, it's the same question in different form.
Retired Moderator V
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If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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St1:
$$x = \frac{y}{|y|}$$
it shows, either x = 1 (when y >0) or -1 (when y <0)
Hence, Not SUFFICIENT

St2:$$|x| = -x$$
It means either x = 0, or x<0
Hence, Not SUFFICIENT

Combining St 1 & 2, x =-1.

SUFFICIENT

gmatbusters wrote:
If $$y ≠ 0$$, is x = -1 ?

(1) $$x = \frac{y}{|y|}$$

(2) $$|x| = -x$$

GMATBuster's Collection

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Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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gmatbusters wrote:
If $$y ≠ 0$$, is x = -1 ?

(1) $$x = \frac{y}{|y|}$$

(2) $$|x| = -x$$

GMATBuster's Collection

(1) if y is -ve, then x =-1 whereas when y is +ve, then x is positive. Insufficient

(2) x is a negative number. insufficient

(1)+(2) only possible value of x is -1. Sufficient

C is correct Re: If y ≠ 0, is x = -1 ? (1) x = y/|y| (2) |x| = -x   [#permalink] 27 Nov 2019, 02:44
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